\newcommand{\txtit}[1]{{\text{\textit{#1}}}}
\def\moves{\txtit{Moves}} % set of all moves
\def\mov{\Gamma} % move assignment 
\def\stra{\pi} % strategy
\def\Stra{\Pi} % set of strategies

\def\straa{\stra_1} % strategy 
\def\strab{\stra_2} % strategy 
\def\Straa{\Stra_1} % set of strategies
\def\Strab{\Stra_2} % set of strategies
\def\path{\sigma}
\def\Paths{\Sigma}

\def\trans{\delta} % prob trans of game
\def\dest{{\text{\textrm{Dest}}}} 
\def\ddest{\tau} % deterministic destination
\def\outcomes{{\text{\textit{Outcomes}}}} % set of outcomes
\def\game{G}
\def\distr{{\text{\textrm{Dist}}}}
\def\dis{\cald}
\def\udis{\calu}
\def\ddis{\mov}
\def\qdis{{\calc}}
\def\AP{\calq}
\def\randstate{{\Theta}}
\def\turn{{\text{\textit{turn}}}}
\def\int#1{[#1]}
\def\set#1{\{#1\}}
\def\altro{\sim}
\def\kstar{k^{\star}}
\newcommand{\ve}{\varepsilon}

% local state equivalence
\newcommand{\loceq}{\equiv}

%propositional distance
\newcommand{\propdist}{{p}}

% to convert a relation into a metric
\newcommand{\D}[1]{\langle\!\langle #1 \rangle\!\rangle}

% generic relation
\newcommand{\rel}{\:R\:}

% transpose of a metric
\newcommand{\transp}{\curvearrowleft}

% To get bold from braindead latex
\newcommand{\imeanbb}[1]{\mbox{\bf #1}}

% various math
\newcommand{\notimplies}{\;\;\;{\not\!\!\!\implies}}
\newcommand{\ii}{i}
\newcommand{\jj}{{\altro i}}
\newcommand{\lb}{\theta_1}
\newcommand{\rb}{\theta_2}

\newcommand{\Sup}{\sup}
\newcommand{\Inf}{\mathop{\rlap{\phantom p}\inf}}
\newcommand{\Max}{\displaystyle\max}
\newcommand{\Min}{\displaystyle\min}
% Variables and such for the game structure
\newcommand{\vars}{\calv}
\newcommand{\varx}{v}
% Variables for the mu-calculus
\newcommand{\mvar}{V}
\newcommand{\mvars}{\mbox{\it MVars}}
\newcommand{\xenv}{\xi}
\newcommand{\penv}{\calp}
\newcommand{\sem}[1]{[\![#1]\!]}
\newcommand{\dsem}[1]{[\![#1]\!]^\Gamma}
% \newcommand{\param}{\alpha}
\newcommand{\params}{\Lambda}

% \valuations and their operators
\newcommand{\valu}{f}
\newcommand{\valub}{g}
\newcommand{\valus}{\calf}
\newcommand{\metrsp}{\calm}
\newcommand{\imax}{\sqcup}
\newcommand{\imin}{\sqcap}
\newcommand{\pre}{{\text{\textrm{Pre}}}}
\newcommand{\qpre}{{\text{\textrm{pre}}}}
\newcommand{\dpre}{\text{\textrm{Pre}}^\Gamma}
% \newcommand{\apre}{\alpha \cdot {\text{\textrm{Pre}}}}
% \newcommand{\aqpre}{\alpha \cdot {\text{\textrm{pre}}}}

%\newcommand{\E}{\cale}
\newcommand{\F}{\calf}
\renewcommand{\P}{\mathbb{P}}
\newcommand{\E}{\mathbb{E}}

% Quantitative mu-calculus
\newcommand{\qmu}{{q\mu}}

% Discounted mu-calculus
\newcommand{\dmu}{{d\mu}}

% Discounted distance
% \newcommand{\da}{d^\alpha}
% \newcommand{\va}{v^\alpha}

% Discounted rewards
% \newcommand{\dfactor}{\alpha}
\newcommand{\drew}{v^\dfactor}
\newcommand{\rew}{v}
\newcommand{\trew}{v^T}
\newcommand{\otrew}{w^T}
\newcommand{\odrew}{w^\dfactor}
\newcommand{\orew}{w}

% Metric
\newcommand{\metr}[1]{[#1]}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% GAME RELATIONS
%
% Please keep these in order, and insert new ones in the appropriate
% places. 

\makeatletter

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% game bisimulations 

% BOOLEAN 

\newcommand{\altbis}{\simeq}
\newcommand{\altbisdet}{\cong^{\mov}}
\newcommand{\altbisran}{\cong^{\dis}}

% DISCOUNTED BOOLEAN

% \newcommand{\daltbis}{\simeq^{\alpha}}

% QUANTITATIVE

% basic symbols 
\newcommand{\@priobis}{\simeq}
\newcommand{\@notpriobis}{\not\simeq}
\newcommand{\@postbis}{\cong}
\newcommand{\@notpostbis}{\not\cong}

\newcommand{\priobis}{\@priobis}
\newcommand{\postbis}{\cong}
%\newcommand{\postbis}{\@postbis}

% DISCOUNTED QUANTITATIVE

% basic symbols 
% No discounting in this paper. 
% \newcommand{\@dpriobis}{\simeq^\alpha}
% \newcommand{\@dnotpriobis}{\not\simeq^\alpha}
% \newcommand{\@dpostbis}{\cong^\alpha}
% \newcommand{\@dnotpostbis}{\not\cong^\alpha}

\newcommand{\dpriobis}{\@dpriobis}
\newcommand{\dpostbis}{\@dpostbis}

% a priori
\newcommand{\priobisran}{\@priobis}
\newcommand{\notpriobisran}{\@notpriobis}
%\newcommand{\priobisdet}{\@priobis^d}
%\newcommand{\notpriobisdet}{\@notpriobis^d}

% without prio/post = a priori
\newcommand{\bisran}{\@priobis}
% \newcommand{\bisdet}{\@priobis^d}

% a posteriori
\newcommand{\postbisran}{\@postbis}
\newcommand{\notpostbisran}{\@notpostbis}
%\newcommand{\postbisdet}{\@postbis^d}
%\newcommand{\notpostbisdet}{\@notpostbis^d}

% superscript for one-mdp definitions
\newcommand{\mdp}{\txtit{1MDP}}
\newcommand{\post}{\txtit{post}}
\newcommand{\prio}{\txtit{prio}}
\newcommand{\Hmdppost}{H^\mdp_\post}
\newcommand{\Hmdpprio}{H^\mdp_\prio}

% TOTAL REWARD QUANTITATIVE

% basic symbols 
\newcommand{\@tpriobis}{\bowtie}
\newcommand{\@nottpriobis}{\not\bowtie}
\newcommand{\@tpostbis}{\widehat\cong}
\newcommand{\@nottpostbis}{\not\widehat\cong}

\newcommand{\tpriobis}{\@tpriobis}
\newcommand{\tpostbis}{\widehat\cong}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% game simulations

% BOOLEAN 

\newcommand{\altsim}{\preceq}
\newcommand{\altsimdet}{\sqsubseteq^{\mov}}
\newcommand{\altsimran}{\sqsubseteq^{\dis}}
\newcommand{\altmis}{\succeq}
\newcommand{\altmisdet}{\sqsubseteq^{\mov}}
\newcommand{\altmisran}{\sqsubseteq^{\dis}}

% QUANTITATIVE

% Basic symbols 
\newcommand{\@postsim}{\sqsubseteq}
\newcommand{\@postmis}{\sqsupseteq}
\newcommand{\@priosim}{\preceq}
\newcommand{\@priomis}{\succeq}

\newcommand{\postsim}{\@postsim}
\newcommand{\postmis}{\@postmis}
\newcommand{\priosim}{\@priosim}
\newcommand{\priomis}{\@priomis}

% DISCOUNTED QUANTITATIVE

% Basic symbols 
% \newcommand{\@dpostsim}{\@postsim^\alpha}
% \newcommand{\@dpostmis}{\@postmis^\alpha}
% \newcommand{\@dpriosim}{\priosim^\alpha}
% \newcommand{\@dpriomis}{\priomis^\alpha}

% \newcommand{\dpostsim}{\@dpostsim}
% \newcommand{\dpostmis}{\@dpostmis}
% \newcommand{\dpriosim}{\@dpriosim}
% \newcommand{\dpriomis}{\@dpriomis}

% a priori
\newcommand{\priosimran}{\@priosim}
%\newcommand{\priosimdet}{\@priosim^d}
% and in the reverse direction
\newcommand{\priomisran}{\@priomis}
%\newcommand{\priomisdet}{\@priomis^d}

% without prio/post = a priori
\newcommand{\simran}{\@priosim}
%\newcommand{\simdet}{\@priosim^d}
\newcommand{\misran}{\@priomis}
%\newcommand{\misdet}{\@priomis^d}

% a posteriori
\newcommand{\postsimran}{\@postsim}
%\newcommand{\postsimdet}{\@postsim^d}

% On MDPs
\newcommand{\eqmdp}{\sim}

% On complexity
\newcommand{\bigo}{\textit{\textbf{O}}}

% TOTAL REWARD QUANTITATIVE

% basic symbols 
%\newcommand{\@tpostsim}{\@\widehat{\postsim}}
%\newcommand{\@tpostmis}{\@\widehat{\postmis}}
%\newcommand{\@tpriosim}{\widehat{\priosim}}
%\newcommand{\@tpriomis}{\widehat{\priomis}}
\newcommand{\@tpriosim}{\unlhd}
\newcommand{\@tpriomis}{\unrhd}

\newcommand{\tpostsim}{\@tpostsim}
\newcommand{\tpostmis}{\@tpostmis}
\newcommand{\tpriosim}{\@tpriosim}
\newcommand{\tpriomis}{\@tpriomis}

\newcommand{\OneStep}{\mathsf{OneStep}}
\newcommand{\IsDistribution}{\mathsf{IsDist}}
\newcommand{\IsValidValuation}{\mathsf{kBounded}}
\newcommand{\PropDistance}{\mathsf{PropDist}}
\newcommand{\APrioriOneStepDistance}{\mathsf{APrioriOneStepDist}}
\newcommand{\APostOneStepDistance}{\mathsf{APostOneStepDist}}
\newcommand{\APrioriExactDistance}{\mathsf{APrioriExactDist}}
\newcommand{\Pseudo}{\mathsf{Pseudo}}
\newcommand{\fp}{\mathsf{Fixpoint}}
\newcommand{\lfp}{\mathsf{LeastFixpoint}}
\newcommand{\lambdavec}{\mathsf{\lambda}}
\newcommand{\OneBis}{\mathsf{OneStepBis}}
\newcommand{\LPF}{\mathsf{LPF}}

\newcommand{\authors}{\ensuremath{\mathbb{A}}}
\newcommand{\pages}{\ensuremath{\mathbb{P}}}
\newcommand{\revisions}{\ensuremath{\mathbb{R}}}
\newcommand{\userrep}{\mathit{UserRep}}

\newcommand{\repexact}{\mathsf{ExactReputation}}
\newcommand{\rep}{\ensuremath{\mathsf{Reputation}}\xspace}
\newcommand{\numedits}{\ensuremath{\mathsf{NumEdits}}\xspace}
\newcommand{\textonly}{\ensuremath{\mathsf{TextOnly}}\xspace}
\newcommand{\editonly}{\ensuremath{\mathsf{EditOnly}}\xspace}
\newcommand{\textlong}{\ensuremath{\mathsf{TextLongevity}}\xspace}
\newcommand{\editlong}{\ensuremath{\mathsf{EditLongevity}}\xspace}
\newcommand{\punish}{\ensuremath{\mathsf{TextLongevityWithPenalty}}\xspace}
\newcommand{\tenrevs}{\ensuremath{\mathsf{TenRevisions}}\xspace}
\newcommand{\elong}{\mathit{ELong}}
\newcommand{\avgspecQ}{\mathit{AvgSpecQ}}
\newcommand{\editlonga}{\mathsf{EditLongevity_A}}
\newcommand{\punisha}{\mathsf{TextLongevityWithPenalty_A}}

\newcommand{\editquality}{\ensuremath{\alpha_{edit}}}
\newcommand{\avgeditquality}{\ensuremath{{\overline{\alpha}}_{edit}}}
\newcommand{\textquality}{\ensuremath{\alpha_{text}}}
\newcommand{\textlongevity}{\ensuremath{\beta_{text}}}

\newcommand{\intro}[1]{\index{#1}{\emph{#1}}}

\makeatother
